A Tunable Graph Model for Incorporating Geographic Spread in Social Graph Models

Modeling and understanding social network structure has interested researchers from many backgrounds including social science, computer science, theoretical physics and graph theory. Notable models include [1] and [2] achieving graphs with power-law degree distribution using preferential attachment and small-world characteristics using randomized rewiring of a regular ring lattice respectively. In contrast to a body of follow-up research which refine upon these seminal works to better capture the graph structure and characteristics (such as improving clustering coefficient by considering social triads along with preferential attachment [3]), this work aims additionally to model the geographic spread in social networks. With increased mobility in our society as well as enhanced communication opportunities social networks are increasingly spread all over the globe. Synthetic graphs imitating real-world social network characteristics are often used for driving simulations for planning and decision support. Incorporating geographic spread can facilitate better infrastructure provisioning in distributed systems supporting social and collaborative applications or model information of malware diffusion, word-of-mouth marketing, etc. The proposed model is tunable and modular. The model can be tuned to produce graphs with different geographic spread. The model is modular in the sense that existing geographic spread agnostic social network models can be plugged into our model to achieve desirable geographic spread in addition to other characteristics (such as degree distribution, clustering coefficient) that such a model would natively support.